Evaluation of material imbalance (a Rybka secret?)

[Alessandro Scotti]

The server crashed (for the second time this year). If it's not back up in a few hours I will upload the files to a different location.

[Edsel Apostol]

Hi Harald,

That is a good idea. I'm just wondering what would be the best way to solve for the material signature?

[hgm]

I don't really believe in analyzing GM games. You never know how much compensation there was for the material imbalance.

So I am generating the games myself, starting from an opening position (pieces behind a closed rank of Pawns). Black and white get the same piece array, like in FRC or CRC. So apart from the move advantage, the situation is totally symmetric. And the move advantage I eliminate by playing each position with both black and white.

And then I simply delete the material I want to compare from the opening position. So if I want to know, say, the chances of R+R vs Q, for each randomly shuffled opening I delete the white Rooks and the black Queen to generate one starting position, and the black Rooks and the white Queen to generate another. You can then play each position a number of times, by the same or by different engines.

If you want to do this with engines that don't support FRC-style castling, you can keep the King and Rooks in the usual place during shuffling, and of course you want the Bishops on unlike colors always. This leaves only 18 positions (for both black and white) in normal Chess, but there are plenty of different engines you can play them with. With Capablanca, you get 216 different positions per color, which is enough variety even if you have only one engine.

[CRoberson]

There is much I like about your idea, but it has holes.
In many cases, it is more about where the pieces are than just what
they are. However, I think there is much to be said for your idea.

I think it applies most in the middilegame or opening. The holes that
I can think of are mostly in the endgame, but they exist in the
opening and middlegame as well.

Mathematically, it comes down to this: can one produce a generalized
description of a position that covers several positions (a many to one
mapping) and yet the description is precise enough to be reasonably
accurate. I believe more than raw piece count is required. Just look
at the suffication games of Nimzovitch.

[hgm]

What you are bringing up is related to the question how to fill the piece-square tables, not so much piece values. Of course the values in PST (or mobilities, for those using mobility evaluation) should be added to the piece values.

What I am measuring is opening-value of the pieces. I assume that the the poor squares the pieces start on (PST-wise) will be quickly forgotten during the development phase: the opponent has no way to pin down your pieces on these poor squares, as he is undeveloped himself. So the pieces will find their way to a much better square. Probably not the best, as the opponent will be able to prevent that, but say somewhere at 75% of the scale from the worst PST value to the best, for that piece. For Rooks I assume that the Rook will be able to find its way to an open file (so the measured piece value is assumed to be the base value plus open-file bonus), but not on the 7th rank.

When there is a suspicion that the value of a piece is strongly dependent on the game-stage, or on the number of Pawns, I sometimes apply a similar method to such positions. E.g. give both sides 5 Pawns (2 on the Q wing, 3 on the K wing) on the second rank, tug their King safely away behind that on the K-wing, and then only add the material you want to compare in a rather inactive position on the back rank, without any other material being present.

It is important to measure the pieces always in the presence of sufficient Pawns, as Chess is basically a game that is decided by pushing Pawns to promotion. So mating potential against a bare King actually says very little about the piece value.

[bob]

What you are bringing up is related to the question how to fill the piece-square tables, not so much piece values. Of course the values in PST (or mobilities, for those using mobility evaluation) should be added to the piece values.

What I am measuring is opening-value of the pieces. I assume that the the poor squares the pieces start on (PST-wise) will be quickly forgotten during the development phase: the opponent has no way to pin down your pieces on these poor squares, as he is undeveloped himself. So the pieces will find their way to a much better square. Probably not the best, as the opponent will be able to prevent that, but say somewhere at 75% of the scale from the worst PST value to the best, for that piece. For Rooks I assume that the Rook will be able to find its way to an open file (so the measured piece value is assumed to be the base value plus open-file bonus), but not on the 7th rank.

When there is a suspicion that the value of a piece is strongly dependent on the game-stage, or on the number of Pawns, I sometimes apply a similar method to such positions. E.g. give both sides 5 Pawns (2 on the Q wing, 3 on the K wing) on the second rank, tug their King safely away behind that on the K-wing, and then only add the material you want to compare in a rather inactive position on the back rank, without any other material being present.

It is important to measure the pieces always in the presence of sufficient Pawns, as Chess is basically a game that is decided by pushing Pawns to promotion. So mating potential against a bare King actually says very little about the piece value.

Your assumption is not always correct. It is not that uncommon to have a bishop stuck on its starting square in some openings, if they are not played accurately. You have to be able to handle those cases as well.

[Pradu]

Now for the help request! I have several questions...
3) if the approach is good, what could be a good way for an engine to use this data?

Convert the probability back to a material value

This could help:
http://chessprogramming.wikispaces.com/ ... 2C+and+ELO

[Alessandro Scotti]

This could help:
http://chessprogramming.wikispaces.com/ ... 2C+and+ELO

Hi Pradu, interesting data. I have prepared a similar table myself but so far I could not find a way to put it in Hamsters without hurting the engine strength.

[Allard Siemelink]

Now for the help request! I have several questions...
3) if the approach is good, what could be a good way for an engine to use this data?

Convert the probability back to a material value

This could help:
http://chessprogramming.wikispaces.com/ ... 2C+and+ELO

So you found that a pawn is worth ~100 elo points on average?

I can confirm that with my own studies.
I also found that the value of a pawn depends on the other
material present on the board.
According to my calculations, the value of an extra pawn seems to range
from ~50 elo points during the opening to ~170 points in the far endgame.

I have yet to make good use of these findings though.

[hgm]

Self-play of Rybka suggest that Pawn odds (in the opening) is worth 171 Elo points, though (73% score).

In general I also find a value much above 50 Elo in the opening (e.g. 63% ~ 100 Elo with micro-Max at 40/2' on 2.4GHz C2D).